LMFDB - Embedded newform 369.2.u.a.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			172.1
Character	$\chi$	$=$	369.172
Dual form			369.2.u.a.118.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.746800 + 1.02788i) q^{2} +(0.119203 + 0.366868i) q^{4} +(3.27974 - 1.06565i) q^{5} +(1.70635 + 0.270260i) q^{7} +(-2.88281 - 0.936683i) q^{8} +O(q^{10})$	\(q+(-0.746800 + 1.02788i) q^{2} +(0.119203 + 0.366868i) q^{4} +(3.27974 - 1.06565i) q^{5} +(1.70635 + 0.270260i) q^{7} +(-2.88281 - 0.936683i) q^{8} +(-1.35394 + 4.16701i) q^{10} +(3.99164 - 2.03384i) q^{11} +(-0.380129 - 2.40004i) q^{13} +(-1.55210 + 1.55210i) q^{14} +(2.49153 - 1.81020i) q^{16} +(0.138725 + 0.272263i) q^{17} +(0.274489 - 1.73306i) q^{19} +(0.781908 + 1.07620i) q^{20} +(-0.890407 + 5.62181i) q^{22} +(-3.75048 - 2.72488i) q^{23} +(5.57599 - 4.05119i) q^{25} +(2.75084 + 1.40162i) q^{26} +(0.104252 + 0.658222i) q^{28} +(-4.39273 + 8.62121i) q^{29} +(-2.28469 + 7.03157i) q^{31} -2.14948i q^{32} +(-0.383454 - 0.0607331i) q^{34} +(5.88439 - 0.931996i) q^{35} +(2.28152 + 7.02179i) q^{37} +(1.57639 + 1.57639i) q^{38} -10.4531 q^{40} +(5.99000 + 2.26271i) q^{41} +(-1.53275 + 2.10964i) q^{43} +(1.22197 + 1.22197i) q^{44} +(5.60172 - 1.82011i) q^{46} +(-6.25754 + 0.991097i) q^{47} +(-3.81880 - 1.24080i) q^{49} +8.75689i q^{50} +(0.835185 - 0.425548i) q^{52} +(0.556161 - 1.09153i) q^{53} +(10.9242 - 10.9242i) q^{55} +(-4.66595 - 2.37742i) q^{56} +(-5.58110 - 10.9535i) q^{58} +(-2.66945 - 1.93947i) q^{59} +(-0.655043 - 0.901590i) q^{61} +(-5.52141 - 7.59957i) q^{62} +(7.19247 + 5.22564i) q^{64} +(-3.80433 - 7.46641i) q^{65} +(-9.09493 - 4.63410i) q^{67} +(-0.0833482 + 0.0833482i) q^{68} +(-3.43648 + 6.74448i) q^{70} +(-0.475905 + 0.242486i) q^{71} -8.56300i q^{73} +(-8.92141 - 2.89874i) q^{74} +(0.668523 - 0.105884i) q^{76} +(7.36081 - 2.39167i) q^{77} +(-6.09837 - 6.09837i) q^{79} +(6.24253 - 8.59210i) q^{80} +(-6.79914 + 4.46722i) q^{82} -9.88122 q^{83} +(0.745119 + 0.745119i) q^{85} +(-1.02381 - 3.15096i) q^{86} +(-13.4122 + 2.12429i) q^{88} +(14.4489 + 2.28848i) q^{89} -4.19804i q^{91} +(0.552606 - 1.70075i) q^{92} +(3.65440 - 7.17217i) q^{94} +(-0.946582 - 5.97648i) q^{95} +(8.80540 + 4.48657i) q^{97} +(4.12728 - 2.99864i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.746800	+	1.02788i	−0.528067	+	0.726822i	−0.986834	−	0.161734i	$-0.948291\pi$
$2$	−0.746800	+	1.02788i	−0.528067	+	0.726822i	0.458767	+	0.888557i	$0.348291\pi$
$3$		0			0
$3$		0			0
$4$	0.119203	+	0.366868i	0.0596014	+	0.183434i
$5$	3.27974	−	1.06565i	1.46674	−	0.476574i	0.536621	−	0.843823i	$-0.319700\pi$
$5$	3.27974	−	1.06565i	1.46674	−	0.476574i	0.930123	+	0.367249i	$0.119700\pi$
$6$		0			0
$7$	1.70635	+	0.270260i	0.644940	+	0.102149i	0.470332	−	0.882489i	$-0.344134\pi$
$7$	1.70635	+	0.270260i	0.644940	+	0.102149i	0.174608	+	0.984638i	$0.444134\pi$
$8$	−2.88281	−	0.936683i	−1.01923	−	0.331167i
$9$		0			0
$10$	−1.35394	+	4.16701i	−0.428155	+	1.31773i
$11$	3.99164	−	2.03384i	1.20352	−	0.613226i	0.266955	−	0.963709i	$-0.413982\pi$
$11$	3.99164	−	2.03384i	1.20352	−	0.613226i	0.936569	+	0.350483i	$0.113982\pi$
$12$		0			0
$13$	−0.380129	−	2.40004i	−0.105429	−	0.665651i	−0.982637	−	0.185540i	$-0.940597\pi$
$13$	−0.380129	−	2.40004i	−0.105429	−	0.665651i	0.877208	−	0.480111i	$-0.159403\pi$
$14$	−1.55210	+	1.55210i	−0.414816	+	0.414816i
$15$		0			0
$16$	2.49153	−	1.81020i	0.622883	−	0.452551i
$17$	0.138725	+	0.272263i	0.0336457	+	0.0660334i	0.907217	−	0.420662i	$-0.138202\pi$
$17$	0.138725	+	0.272263i	0.0336457	+	0.0660334i	−0.873572	+	0.486695i	$0.838202\pi$
$18$		0			0
$19$	0.274489	−	1.73306i	0.0629721	−	0.397590i	−0.935989	−	0.352028i	$-0.885492\pi$
$19$	0.274489	−	1.73306i	0.0629721	−	0.397590i	0.998962	−	0.0455621i	$-0.0145079\pi$
$20$	0.781908	+	1.07620i	0.174840	+	0.240646i
$21$		0			0
$22$	−0.890407	+	5.62181i	−0.189835	+	1.19857i
$23$	−3.75048	−	2.72488i	−0.782029	−	0.568178i	0.123558	−	0.992337i	$-0.460569\pi$
$23$	−3.75048	−	2.72488i	−0.782029	−	0.568178i	−0.905587	+	0.424160i	$0.860569\pi$
$24$		0			0
$25$	5.57599	−	4.05119i	1.11520	−	0.810239i
$26$	2.75084	+	1.40162i	0.539483	+	0.274880i
$27$		0			0
$28$	0.104252	+	0.658222i	0.0197018	+	0.124392i
$29$	−4.39273	+	8.62121i	−0.815709	+	1.60092i	−0.0165007	+	0.999864i	$0.505253\pi$
$29$	−4.39273	+	8.62121i	−0.815709	+	1.60092i	−0.799208	+	0.601055i	$0.794747\pi$
$30$		0			0
$31$	−2.28469	+	7.03157i	−0.410343	+	1.26291i	0.506007	+	0.862529i	$0.331121\pi$
$31$	−2.28469	+	7.03157i	−0.410343	+	1.26291i	−0.916350	+	0.400378i	$0.868879\pi$
$32$		−	2.14948i		−	0.379978i
$33$		0			0
$34$	−0.383454	−	0.0607331i	−0.0657618	−	0.0104156i
$35$	5.88439	−	0.931996i	0.994644	−	0.157536i
$36$		0			0
$37$	2.28152	+	7.02179i	0.375079	+	1.15438i	0.943425	+	0.331585i	$0.107583\pi$
$37$	2.28152	+	7.02179i	0.375079	+	1.15438i	−0.568346	+	0.822790i	$0.692417\pi$
$38$	1.57639	+	1.57639i	0.255724	+	0.255724i
$39$		0			0
$40$	−10.4531			−1.65277
$41$	5.99000	+	2.26271i	0.935481	+	0.353376i
$41$	5.99000	+	2.26271i	0.935481	+	0.353376i
$42$		0			0
$43$	−1.53275	+	2.10964i	−0.233742	+	0.321718i	−0.909735	−	0.415190i	$-0.863715\pi$
$43$	−1.53275	+	2.10964i	−0.233742	+	0.321718i	0.675993	+	0.736908i	$0.263715\pi$
$44$	1.22197	+	1.22197i	0.184218	+	0.184218i
$45$		0			0
$46$	5.60172	−	1.82011i	0.825928	−	0.268360i
$47$	−6.25754	+	0.991097i	−0.912756	+	0.144566i	−0.595111	−	0.803643i	$-0.702892\pi$
$47$	−6.25754	+	0.991097i	−0.912756	+	0.144566i	−0.317645	+	0.948210i	$0.602892\pi$
$48$		0			0
$49$	−3.81880	−	1.24080i	−0.545543	−	0.177258i
$50$			8.75689i			1.23841i
$51$		0			0
$52$	0.835185	−	0.425548i	0.115819	−	0.0590129i
$53$	0.556161	−	1.09153i	0.0763946	−	0.149933i	−0.849650	−	0.527347i	$-0.823187\pi$
$53$	0.556161	−	1.09153i	0.0763946	−	0.149933i	0.926045	+	0.377414i	$0.123187\pi$
$54$		0			0
$55$	10.9242	−	10.9242i	1.47301	−	1.47301i
$56$	−4.66595	−	2.37742i	−0.623513	−	0.317696i
$57$		0			0
$58$	−5.58110	−	10.9535i	−0.732834	−	1.43827i
$59$	−2.66945	−	1.93947i	−0.347533	−	0.252497i	0.400300	−	0.916384i	$-0.368906\pi$
$59$	−2.66945	−	1.93947i	−0.347533	−	0.252497i	−0.747833	+	0.663887i	$0.768906\pi$
$60$		0			0
$61$	−0.655043	−	0.901590i	−0.0838697	−	0.115437i	0.765021	−	0.644006i	$-0.222729\pi$
$61$	−0.655043	−	0.901590i	−0.0838697	−	0.115437i	−0.848890	+	0.528569i	$0.822729\pi$
$62$	−5.52141	−	7.59957i	−0.701220	−	0.965147i
$63$		0			0
$64$	7.19247	+	5.22564i	0.899059	+	0.653205i
$65$	−3.80433	−	7.46641i	−0.471869	−	0.926095i
$66$		0			0
$67$	−9.09493	−	4.63410i	−1.11112	−	0.566145i	−0.200628	−	0.979667i	$-0.564298\pi$
$67$	−9.09493	−	4.63410i	−1.11112	−	0.566145i	−0.910494	+	0.413522i	$0.864298\pi$
$68$	−0.0833482	+	0.0833482i	−0.0101075	+	0.0101075i
$69$		0			0
$70$	−3.43648	+	6.74448i	−0.410738	+	0.806119i
$71$	−0.475905	+	0.242486i	−0.0564795	+	0.0287777i	−0.482002	−	0.876170i	$-0.660090\pi$
$71$	−0.475905	+	0.242486i	−0.0564795	+	0.0287777i	0.425523	+	0.904948i	$0.360090\pi$
$72$		0			0
$73$		−	8.56300i		−	1.00222i	−0.865383	−	0.501112i	$-0.832925\pi$
$73$		−	8.56300i		−	1.00222i	0.865383	−	0.501112i	$-0.167075\pi$
$74$	−8.92141	−	2.89874i	−1.03709	−	0.336972i
$75$		0			0
$76$	0.668523	−	0.105884i	0.0766848	−	0.0121457i
$77$	7.36081	−	2.39167i	0.838842	−	0.272556i
$78$		0			0
$79$	−6.09837	−	6.09837i	−0.686120	−	0.686120i	0.275252	−	0.961372i	$-0.411239\pi$
$79$	−6.09837	−	6.09837i	−0.686120	−	0.686120i	−0.961372	+	0.275252i	$0.911239\pi$
$80$	6.24253	−	8.59210i	0.697936	−	0.960626i
$81$		0			0
$82$	−6.79914	+	4.46722i	−0.750839	+	0.493322i
$83$	−9.88122			−1.08460			−0.542302	−	0.840183i	$-0.682447\pi$
$83$	−9.88122			−1.08460			−0.542302	+	0.840183i	$0.682447\pi$
$84$		0			0
$85$	0.745119	+	0.745119i	0.0808195	+	0.0808195i
$86$	−1.02381	−	3.15096i	−0.110400	−	0.339777i
$87$		0			0
$88$	−13.4122	+	2.12429i	−1.42975	+	0.226450i
$89$	14.4489	+	2.28848i	1.53158	+	0.242579i	0.864587	−	0.502483i	$-0.167580\pi$
$89$	14.4489	+	2.28848i	1.53158	+	0.242579i	0.666996	+	0.745062i	$0.267580\pi$
$90$		0			0
$91$		−	4.19804i		−	0.440074i
$92$	0.552606	−	1.70075i	0.0576131	−	0.177315i
$93$		0			0
$94$	3.65440	−	7.17217i	0.376923	−	0.739753i
$95$	−0.946582	−	5.97648i	−0.0971172	−	0.613174i
$96$		0			0
$97$	8.80540	+	4.48657i	0.894053	+	0.455543i	0.839745	−	0.542982i	$-0.182705\pi$
$97$	8.80540	+	4.48657i	0.894053	+	0.455543i	0.0543082	+	0.998524i	$0.482705\pi$
$98$	4.12728	−	2.99864i	0.416918	−	0.302909i
$99$		0			0
$100$	2.15093	+	1.56274i	0.215093	+	0.156274i
$101$	−0.271981	+	1.71722i	−0.0270631	+	0.170870i	−0.997518	−	0.0704133i	$-0.977568\pi$
$101$	−0.271981	+	1.71722i	−0.0270631	+	0.170870i	0.970455	+	0.241283i	$0.0775682\pi$
$102$		0			0
$103$	4.97027	+	6.84100i	0.489736	+	0.674063i	0.980339	−	0.197320i	$-0.0632236\pi$
$103$	4.97027	+	6.84100i	0.489736	+	0.674063i	−0.490603	+	0.871383i	$0.663224\pi$
$104$	−1.15223	+	7.27492i	−0.112986	+	0.713365i
$105$		0			0
$106$	0.706621	+	1.38682i	0.0686331	+	0.134700i
$107$	0.277133	−	0.201349i	0.0267915	−	0.0194651i	−0.574309	−	0.818639i	$-0.694729\pi$
$107$	0.277133	−	0.201349i	0.0267915	−	0.0194651i	0.601100	+	0.799174i	$0.294729\pi$
$108$		0			0
$109$	0.0194034	−	0.0194034i	0.00185851	−	0.00185851i	−0.706177	−	0.708035i	$-0.749582\pi$
$109$	0.0194034	−	0.0194034i	0.00185851	−	0.00185851i	0.708035	+	0.706177i	$0.249582\pi$
$110$	3.07059	+	19.3869i	0.292769	+	1.84847i
$111$		0			0
$112$	4.74065	−	2.41548i	0.447950	−	0.228242i
$113$	1.43672	−	4.42177i	0.135155	−	0.415965i	−0.860459	−	0.509520i	$-0.829823\pi$
$113$	1.43672	−	4.42177i	0.135155	−	0.415965i	0.995614	+	0.0935546i	$0.0298230\pi$
$114$		0			0
$115$	−15.2044	−	4.94020i	−1.41782	−	0.460676i
$116$	−3.68647	−	0.583880i	−0.342280	−	0.0542119i
$117$		0			0
$118$	3.98709	−	1.29548i	0.367041	−	0.119259i
$119$	0.163132	+	0.502068i	0.0149543	+	0.0460245i
$120$		0			0
$121$	5.33103	−	7.33753i	0.484639	−	0.667049i
$122$	1.41591			0.128191
$123$		0			0
$124$	−2.85200			−0.256117
$125$	3.83568	−	5.27936i	0.343074	−	0.472200i
$126$		0			0
$127$	−6.46903	−	19.9096i	−0.574034	−	1.76669i	−0.639446	−	0.768836i	$-0.720836\pi$
$127$	−6.46903	−	19.9096i	−0.574034	−	1.76669i	0.0654117	−	0.997858i	$-0.479164\pi$
$128$	−6.65413	+	2.16206i	−0.588147	+	0.191101i
$129$		0			0
$130$	10.5157	+	1.66552i	0.922285	+	0.146076i
$131$	−13.7334	−	4.46226i	−1.19989	−	0.389869i	−0.360172	−	0.932886i	$-0.617282\pi$
$131$	−13.7334	−	4.46226i	−1.19989	−	0.389869i	−0.839722	+	0.543016i	$0.817282\pi$
$132$		0			0
$133$	0.936750	−	2.88302i	0.0812265	−	0.249990i
$134$	11.5554	−	5.88777i	0.998235	−	0.508626i
$135$		0			0
$136$	−0.144894	−	0.914824i	−0.0124245	−	0.0784455i
$137$	−0.668766	+	0.668766i	−0.0571365	+	0.0571365i	−0.735098	−	0.677961i	$-0.762864\pi$
$137$	−0.668766	+	0.668766i	−0.0571365	+	0.0571365i	0.677961	+	0.735098i	$0.262864\pi$
$138$		0			0
$139$	−6.13162	+	4.45488i	−0.520077	+	0.377858i	−0.816633	−	0.577157i	$-0.804162\pi$
$139$	−6.13162	+	4.45488i	−0.520077	+	0.377858i	0.296556	+	0.955016i	$0.404162\pi$
$140$	1.04336	+	2.04770i	0.0881796	+	0.173062i
$141$		0			0
$142$	0.106159	−	0.670262i	0.00890868	−	0.0562472i
$143$	−6.39863	−	8.80696i	−0.535081	−	0.736475i
$144$		0			0
$145$	−5.21979	+	32.9564i	−0.433480	+	2.73688i
$146$	8.80175	+	6.39485i	0.728438	+	0.529241i
$147$		0			0
$148$	−2.30411	+	1.67403i	−0.189397	+	0.137605i
$149$	−8.57816	−	4.37079i	−0.702750	−	0.358069i	0.0658226	−	0.997831i	$-0.479033\pi$
$149$	−8.57816	−	4.37079i	−0.702750	−	0.358069i	−0.768573	+	0.639762i	$0.779033\pi$
$150$		0			0
$151$	2.81584	+	17.7785i	0.229150	+	1.44679i	0.787051	+	0.616887i	$0.211607\pi$
$151$	2.81584	+	17.7785i	0.229150	+	1.44679i	−0.557902	+	0.829907i	$0.688393\pi$
$152$	−2.41463	+	4.73897i	−0.195852	+	0.384381i
$153$		0			0
$154$	−3.03869	+	9.35214i	−0.244865	+	0.753617i
$155$			25.4964i			2.04792i
$156$		0			0
$157$	10.9681	+	1.73718i	0.875350	+	0.138642i	0.577912	−	0.816099i	$-0.303868\pi$
$157$	10.9681	+	1.73718i	0.875350	+	0.138642i	0.297438	+	0.954741i	$0.403868\pi$
$158$	10.8227	−	1.71414i	0.861005	−	0.136370i
$159$		0			0
$160$	−2.29060	−	7.04973i	−0.181087	−	0.557330i
$161$	−5.66321	−	5.66321i	−0.446324	−	0.446324i
$162$		0			0
$163$	1.98697			0.155631			0.0778156	−	0.996968i	$-0.475205\pi$
$163$	1.98697			0.155631			0.0778156	+	0.996968i	$0.475205\pi$
$164$	−0.116093	+	2.46726i	−0.00906536	+	0.192661i
$165$		0			0
$166$	7.37930	−	10.1567i	0.572744	−	0.788315i
$167$	−3.26398	−	3.26398i	−0.252574	−	0.252574i	0.569451	−	0.822025i	$-0.307156\pi$
$167$	−3.26398	−	3.26398i	−0.252574	−	0.252574i	−0.822025	+	0.569451i	$0.807156\pi$
$168$		0			0
$169$	6.74805	−	2.19257i	0.519081	−	0.168660i
$170$	−1.32235	+	0.209439i	−0.101420	+	0.0160633i
$171$		0			0
$172$	−0.956669	−	0.310841i	−0.0729453	−	0.0237014i
$173$		−	3.45816i		−	0.262919i	−0.991322	−	0.131460i	$-0.958034\pi$
$173$		−	3.45816i		−	0.262919i	0.991322	−	0.131460i	$-0.0419663\pi$
$174$		0			0
$175$	10.6095	−	5.40580i	0.802001	−	0.408640i
$176$	6.26363	−	12.2931i	0.472139	−	0.926624i
$177$		0			0
$178$	−13.1427	+	13.1427i	−0.985091	+	0.985091i
$179$	14.1878	+	7.22903i	1.06044	+	0.540323i	0.895078	−	0.445909i	$-0.147119\pi$
$179$	14.1878	+	7.22903i	1.06044	+	0.540323i	0.165366	+	0.986232i	$0.447119\pi$
$180$		0			0
$181$	−1.10429	−	2.16728i	−0.0820810	−	0.161093i	0.846318	−	0.532678i	$-0.178814\pi$
$181$	−1.10429	−	2.16728i	−0.0820810	−	0.161093i	−0.928399	+	0.371585i	$0.878814\pi$
$182$	4.31509	+	3.13510i	0.319856	+	0.232389i
$183$		0			0
$184$	8.25959	+	11.3683i	0.608905	+	0.838085i
$185$	14.9656	+	20.5983i	1.10029	+	1.51442i
$186$		0			0
$187$	1.10748	+	0.804630i	0.0809869	+	0.0588404i
$188$	−1.10952	−	2.17755i	−0.0809199	−	0.158814i
$189$		0			0
$190$	6.85003	+	3.49026i	0.496953	+	0.253210i
$191$	4.58243	−	4.58243i	0.331573	−	0.331573i	−0.521610	−	0.853184i	$-0.674669\pi$
$191$	4.58243	−	4.58243i	0.331573	−	0.331573i	0.853184	+	0.521610i	$0.174669\pi$
$192$		0			0
$193$	−0.572698	+	1.12398i	−0.0412237	+	0.0809060i	−0.910700	−	0.413069i	$-0.864457\pi$
$193$	−0.572698	+	1.12398i	−0.0412237	+	0.0809060i	0.869476	+	0.493975i	$0.164457\pi$
$194$	−11.1875	+	5.70034i	−0.803219	+	0.409260i
$195$		0			0
$196$		−	1.54890i		−	0.110636i
$197$	3.22508	+	1.04789i	0.229777	+	0.0746592i	0.421643	−	0.906762i	$-0.361454\pi$
$197$	3.22508	+	1.04789i	0.229777	+	0.0746592i	−0.191865	+	0.981421i	$0.561454\pi$
$198$		0			0
$199$	7.65101	−	1.21180i	0.542365	−	0.0859023i	0.120760	−	0.992682i	$-0.461467\pi$
$199$	7.65101	−	1.21180i	0.542365	−	0.0859023i	0.421605	+	0.906779i	$0.361467\pi$
$200$	−19.8692	+	6.45590i	−1.40497	+	0.456501i
$201$		0			0
$202$	−1.56198	−	1.56198i	−0.109901	−	0.109901i
$203$	−9.82550	+	13.5236i	−0.689615	+	0.949174i
$204$		0			0
$205$	22.0569	+	1.03785i	1.54052	+	0.0724868i
$206$	−10.7435			−0.748538
$207$		0			0
$208$	−5.29166	−	5.29166i	−0.366911	−	0.366911i
$209$	−2.42910	−	7.47600i	−0.168024	−	0.517126i
$210$		0			0
$211$	−15.0249	+	2.37972i	−1.03436	+	0.163826i	−0.650453	−	0.759546i	$-0.725421\pi$
$211$	−15.0249	+	2.37972i	−1.03436	+	0.163826i	−0.383905	+	0.923372i	$0.625421\pi$
$212$	0.466743	+	0.0739248i	0.0320560	+	0.00507717i
$213$		0			0
$214$			0.435228i			0.0297515i
$215$	−2.77886	+	8.55246i	−0.189517	+	0.583273i
$216$		0			0
$217$	−5.79884	+	11.3809i	−0.393651	+	0.772584i
$218$	0.00545394	+	0.0344348i	0.000369387	+	0.00233222i
$219$		0			0
$220$	5.30992	+	2.70554i	0.357995	+	0.182407i
$221$	0.600708	−	0.436440i	0.0404080	−	0.0293581i
$222$		0			0
$223$	−2.35953	−	1.71430i	−0.158006	−	0.114798i	0.505973	−	0.862549i	$-0.331134\pi$
$223$	−2.35953	−	1.71430i	−0.158006	−	0.114798i	−0.663979	+	0.747751i	$0.731134\pi$
$224$	0.580917	−	3.66777i	0.0388142	−	0.245063i
$225$		0			0
$226$	3.47212	+	4.77896i	0.230962	+	0.317892i
$227$	−2.59992	+	16.4153i	−0.172563	+	1.08952i	0.737591	+	0.675248i	$0.235963\pi$
$227$	−2.59992	+	16.4153i	−0.172563	+	1.08952i	−0.910154	+	0.414271i	$0.864037\pi$
$228$		0			0
$229$	5.63479	+	11.0589i	0.372358	+	0.730793i	0.998815	−	0.0486625i	$-0.0154959\pi$
$229$	5.63479	+	11.0589i	0.372358	+	0.730793i	−0.626458	+	0.779455i	$0.715496\pi$
$230$	16.4326	−	11.9390i	1.08353	−	0.787232i
$231$		0			0
$232$	20.7387	−	20.7387i	1.36157	−	1.36157i
$233$	−0.476691	−	3.00971i	−0.0312291	−	0.197173i	0.967141	−	0.254240i	$-0.0818252\pi$
$233$	−0.476691	−	3.00971i	−0.0312291	−	0.197173i	−0.998370	+	0.0570669i	$0.981825\pi$
$234$		0			0
$235$	−19.4669	+	9.91890i	−1.26988	+	0.647038i
$236$	0.393324	−	1.21053i	0.0256032	−	0.0787985i
$237$		0			0
$238$	−0.637893	−	0.207264i	−0.0413485	−	0.0134349i
$239$	13.5302	+	2.14297i	0.875193	+	0.138617i	0.577840	−	0.816150i	$-0.303896\pi$
$239$	13.5302	+	2.14297i	0.875193	+	0.138617i	0.297354	+	0.954767i	$0.403896\pi$
$240$		0			0
$241$	−12.5581	+	4.08039i	−0.808941	+	0.262841i	−0.684149	−	0.729342i	$-0.739826\pi$
$241$	−12.5581	+	4.08039i	−0.808941	+	0.262841i	−0.124792	+	0.992183i	$0.539826\pi$
$242$	3.56091	+	10.9593i	0.228904	+	0.704493i
$243$		0			0
$244$	0.252682	−	0.347786i	0.0161763	−	0.0222647i
$245$	−13.8469			−0.884648
$246$		0			0
$247$	−4.26374			−0.271295
$248$	13.1727	−	18.1307i	0.836467	−	1.15130i
$249$		0			0
$250$	2.56207	+	7.88525i	0.162040	+	0.498707i
$251$	19.8271	−	6.44222i	1.25148	−	0.406630i	0.393027	−	0.919527i	$-0.371428\pi$
$251$	19.8271	−	6.44222i	1.25148	−	0.406630i	0.858450	+	0.512897i	$0.171428\pi$
$252$		0			0
$253$	−20.5125	−	3.24887i	−1.28961	−	0.204255i
$254$	25.2958	+	8.21912i	1.58720	+	0.515713i
$255$		0			0
$256$	−2.74760	+	8.45624i	−0.171725	+	0.528515i
$257$	−16.3088	+	8.30974i	−1.01731	+	0.518348i	−0.881399	−	0.472373i	$-0.843398\pi$
$257$	−16.3088	+	8.30974i	−1.01731	+	0.518348i	−0.135916	+	0.990720i	$0.543398\pi$
$258$		0			0
$259$	1.99537	+	12.5982i	0.123986	+	0.782817i
$260$	2.28570	−	2.28570i	0.141753	−	0.141753i
$261$		0			0
$262$	14.8428	−	10.7839i	0.916991	−	0.666233i
$263$	−9.77669	−	19.1878i	−0.602857	−	1.18317i	−0.967700	−	0.252104i	$-0.918878\pi$
$263$	−9.77669	−	19.1878i	−0.602857	−	1.18317i	0.364844	−	0.931069i	$-0.381122\pi$
$264$		0			0
$265$	0.660875	−	4.17260i	0.0405972	−	0.256321i
$266$	2.26384	+	3.11591i	0.138805	+	0.191049i
$267$		0			0
$268$	0.615963	−	3.88904i	0.0376259	−	0.237561i
$269$	−2.38656	−	1.73394i	−0.145511	−	0.105720i	0.512648	−	0.858599i	$-0.328665\pi$
$269$	−2.38656	−	1.73394i	−0.145511	−	0.105720i	−0.658159	+	0.752879i	$0.728665\pi$
$270$		0			0
$271$	9.08621	−	6.60152i	0.551948	−	0.401014i	−0.276555	−	0.960998i	$-0.589193\pi$
$271$	9.08621	−	6.60152i	0.551948	−	0.401014i	0.828503	+	0.559984i	$0.189193\pi$
$272$	0.838488	+	0.427231i	0.0508408	+	0.0259047i
$273$		0			0
$274$	−0.187978	−	1.18685i	−0.0113562	−	0.0717000i
$275$	14.0179	−	27.5116i	0.845308	−	1.65901i
$276$		0			0
$277$	9.15694	−	28.1822i	0.550187	−	1.69330i	−0.158138	−	0.987417i	$-0.550549\pi$
$277$	9.15694	−	28.1822i	0.550187	−	1.69330i	0.708326	−	0.705886i	$-0.249451\pi$
$278$		−	9.62949i		−	0.577538i
$279$		0			0
$280$	−17.8366	−	2.82504i	−1.06594	−	0.168828i
$281$	−2.43464	+	0.385610i	−0.145239	+	0.0230036i	−0.228630	−	0.973513i	$-0.573425\pi$
$281$	−2.43464	+	0.385610i	−0.145239	+	0.0230036i	0.0833917	+	0.996517i	$0.473425\pi$
$282$		0			0
$283$	−4.97243	−	15.3036i	−0.295580	−	0.909703i	−0.983026	−	0.183467i	$-0.941268\pi$
$283$	−4.97243	−	15.3036i	−0.295580	−	0.909703i	0.687446	−	0.726236i	$-0.258732\pi$
$284$	−0.145689	−	0.145689i	−0.00864507	−	0.00864507i
$285$		0			0
$286$	13.8310			0.817845
$287$	9.60953	+	5.47984i	0.567233	+	0.323465i
$288$		0			0
$289$	9.93747	−	13.6777i	0.584557	−	0.804574i
$290$	−29.9772	−	29.9772i	−1.76032	−	1.76032i
$291$		0			0
$292$	3.14149	−	1.02073i	0.183842	−	0.0597339i
$293$	−26.1450	+	4.14096i	−1.52741	+	0.241917i	−0.862904	−	0.505369i	$-0.831356\pi$
$293$	−26.1450	+	4.14096i	−1.52741	+	0.241917i	−0.664502	+	0.747286i	$0.731356\pi$
$294$		0			0
$295$	−10.8219	−	3.51625i	−0.630075	−	0.204724i
$296$		−	22.3796i		−	1.30079i
$297$		0			0
$298$	10.8988	−	5.55323i	0.631352	−	0.321690i
$299$	−5.11416	+	10.0371i	−0.295759	+	0.580461i
$300$		0			0
$301$	−3.18556	+	3.18556i	−0.183612	+	0.183612i
$302$	−20.3771	−	10.3826i	−1.17257	−	0.597454i
$303$		0			0
$304$	−2.45329	−	4.81485i	−0.140706	−	0.276150i
$305$	−3.10915	−	2.25893i	−0.178030	−	0.129346i
$306$		0			0
$307$	6.74688	+	9.28628i	0.385065	+	0.529996i	0.956917	−	0.290360i	$-0.0937751\pi$
$307$	6.74688	+	9.28628i	0.385065	+	0.529996i	−0.571853	+	0.820356i	$0.693775\pi$
$308$	1.75486	+	2.41535i	0.0999922	+	0.137627i
$309$		0			0
$310$	−26.2073	−	19.0407i	−1.48847	−	1.08144i
$311$	8.36318	+	16.4137i	0.474232	+	0.930733i	0.996936	+	0.0782190i	$0.0249234\pi$
$311$	8.36318	+	16.4137i	0.474232	+	0.930733i	−0.522704	+	0.852514i	$0.675077\pi$
$312$		0			0
$313$	−12.8108	−	6.52744i	−0.724110	−	0.368953i	0.0527652	−	0.998607i	$-0.483197\pi$
$313$	−12.8108	−	6.52744i	−0.724110	−	0.368953i	−0.776875	+	0.629654i	$0.783197\pi$
$314$	−9.97659	+	9.97659i	−0.563012	+	0.563012i
$315$		0			0
$316$	1.51036	−	2.96424i	0.0849642	−	0.166752i
$317$	21.3431	−	10.8749i	1.19875	−	0.610794i	0.263459	−	0.964671i	$-0.415137\pi$
$317$	21.3431	−	10.8749i	1.19875	−	0.610794i	0.935292	+	0.353877i	$0.115137\pi$
$318$		0			0
$319$			43.3469i			2.42696i
$320$	29.1581	+	9.47406i	1.62999	+	0.529616i
$321$		0			0
$322$	10.0504	−	1.59183i	0.560087	−	0.0887091i
$323$	0.509925	−	0.165685i	0.0283730	−	0.00921894i
$324$		0			0
$325$	−11.8426	−	11.8426i	−0.656910	−	0.656910i
$326$	−1.48387	+	2.04237i	−0.0821838	+	0.113116i
$327$		0			0
$328$	−15.1486	−	12.1337i	−0.836442	−	0.669972i
$329$	−10.9454			−0.603441
$330$		0			0
$331$	−0.797529	−	0.797529i	−0.0438362	−	0.0438362i	0.684849	−	0.728685i	$-0.259868\pi$
$331$	−0.797529	−	0.797529i	−0.0438362	−	0.0438362i	−0.728685	+	0.684849i	$0.759868\pi$
$332$	−1.17787	−	3.62511i	−0.0646439	−	0.198954i
$333$		0			0
$334$	5.79252	−	0.917445i	0.316953	−	0.0502004i
$335$	−34.7673	−	5.50660i	−1.89954	−	0.300858i
$336$		0			0
$337$			9.36237i			0.510001i	0.966941	+	0.255000i	$0.0820756\pi$
$337$			9.36237i			0.510001i	−0.966941	+	0.255000i	$0.917924\pi$
$338$	−2.78574	+	8.57362i	−0.151524	+	0.466343i
$339$		0			0
$340$	−0.184540	+	0.362180i	−0.0100081	+	0.0196420i
$341$	5.18142	+	32.7142i	0.280590	+	1.77157i
$342$		0			0
$343$	−16.9561	−	8.63958i	−0.915545	−	0.466494i
$344$	6.39469	−	4.64601i	0.344779	−	0.250496i
$345$		0			0
$346$	3.55458	+	2.58255i	0.191095	+	0.138839i
$347$	1.06889	−	6.74870i	0.0573810	−	0.362289i	−0.942245	−	0.334926i	$-0.891289\pi$
$347$	1.06889	−	6.74870i	0.0573810	−	0.362289i	0.999626	−	0.0273636i	$-0.00871119\pi$
$348$		0			0
$349$	2.17419	+	2.99251i	0.116382	+	0.160185i	0.863233	−	0.504805i	$-0.168436\pi$
$349$	2.17419	+	2.99251i	0.116382	+	0.160185i	−0.746852	+	0.664990i	$0.768436\pi$
$350$	−2.36663	+	14.9423i	−0.126502	+	0.798702i
$351$		0			0
$352$	−4.37170	−	8.57994i	−0.233012	−	0.457312i
$353$	2.84588	−	2.06765i	0.151471	−	0.110050i	−0.509469	−	0.860489i	$-0.670158\pi$
$353$	2.84588	−	2.06765i	0.151471	−	0.110050i	0.660939	+	0.750439i	$0.270158\pi$
$354$		0			0
$355$	−1.30244	+	1.30244i	−0.0691263	+	0.0691263i
$356$	0.882778	+	5.57364i	0.0467872	+	0.295403i
$357$		0			0
$358$	−18.0260	+	9.18472i	−0.952705	+	0.485428i
$359$	4.61076	−	14.1905i	0.243347	−	0.748944i	−0.752557	−	0.658527i	$-0.771180\pi$
$359$	4.61076	−	14.1905i	0.243347	−	0.748944i	0.995904	−	0.0904171i	$-0.0288200\pi$
$360$		0			0
$361$	15.1419	+	4.91991i	0.796944	+	0.258943i
$362$	3.05239	+	0.483452i	0.160430	+	0.0254097i
$363$		0			0
$364$	1.54013	−	0.500418i	0.0807247	−	0.0262290i
$365$	−9.12518	−	28.0844i	−0.477634	−	1.47001i
$366$		0			0
$367$	−10.3592	+	14.2583i	−0.540748	+	0.744276i	−0.988721	−	0.149771i	$-0.952146\pi$
$367$	−10.3592	+	14.2583i	−0.540748	+	0.744276i	0.447972	+	0.894047i	$0.352146\pi$
$368$	−14.2770			−0.744242
$369$		0			0
$370$	−32.3489			−1.68174
$371$	1.24400	−	1.71222i	0.0645854	−	0.0888942i
$372$		0			0
$373$	0.925209	+	2.84750i	0.0479055	+	0.147438i	0.972148	−	0.234368i	$-0.0753022\pi$
$373$	0.925209	+	2.84750i	0.0479055	+	0.147438i	−0.924242	+	0.381806i	$0.875302\pi$
$374$	−1.65413	+	0.537460i	−0.0855330	+	0.0277914i
$375$		0			0
$376$	18.9677	+	3.00418i	0.978183	+	0.154929i
$377$	22.3610	+	7.26554i	1.15165	+	0.374194i
$378$		0			0
$379$	9.87141	−	30.3811i	0.507060	−	1.56057i	−0.290220	−	0.956960i	$-0.593728\pi$
$379$	9.87141	−	30.3811i	0.507060	−	1.56057i	0.797280	−	0.603610i	$-0.206272\pi$
$380$	2.07975	−	1.05968i	0.106689	−	0.0543606i
$381$		0			0
$382$	1.28804	+	8.13236i	0.0659018	+	0.416088i
$383$	−1.77733	+	1.77733i	−0.0908173	+	0.0908173i	−0.751056	−	0.660239i	$-0.770455\pi$
$383$	−1.77733	+	1.77733i	−0.0908173	+	0.0908173i	0.660239	+	0.751056i	$0.270455\pi$
$384$		0			0
$385$	21.5928	−	15.6881i	1.10047	−	0.799540i
$386$	−0.727631	−	1.42806i	−0.0370354	−	0.0726861i
$387$		0			0
$388$	−0.596354	+	3.76523i	−0.0302753	+	0.191151i
$389$	20.3807	+	28.0517i	1.03334	+	1.42228i	0.902406	+	0.430886i	$0.141799\pi$
$389$	20.3807	+	28.0517i	1.03334	+	1.42228i	0.130938	+	0.991391i	$0.458201\pi$
$390$		0			0
$391$	0.221600	−	1.39913i	0.0112068	−	0.0707568i
$392$	9.84665	+	7.15401i	0.497331	+	0.361332i
$393$		0			0
$394$	−3.48560	+	2.53244i	−0.175602	+	0.127582i
$395$	−26.4998	−	13.5023i	−1.33335	−	0.679376i
$396$		0			0
$397$	5.37624	+	33.9443i	0.269826	+	1.70361i	0.634867	+	0.772622i	$0.281055\pi$
$397$	5.37624	+	33.9443i	0.269826	+	1.70361i	−0.365041	+	0.930992i	$0.618945\pi$
$398$	−4.46818	+	8.76931i	−0.223970	+	0.439566i
$399$		0			0
$400$	6.55927	−	20.1874i	0.327963	−	1.00937i
$401$			8.02435i			0.400717i	0.979723	+	0.200359i	$0.0642107\pi$
$401$			8.02435i			0.400717i	−0.979723	+	0.200359i	$0.935789\pi$
$402$		0			0
$403$	17.7445	+	2.81045i	0.883917	+	0.139999i
$404$	−0.662414	+	0.104916i	−0.0329563	+	0.00521977i
$405$		0			0
$406$	−6.56302	−	20.1989i	−0.325717	−	1.00246i
$407$	23.3882	+	23.3882i	1.15931	+	1.15931i
$408$		0			0
$409$	6.97227			0.344757			0.172378	−	0.985031i	$-0.444855\pi$
$409$	6.97227			0.344757			0.172378	+	0.985031i	$0.444855\pi$
$410$	−17.5389	+	21.8968i	−0.866184	+	1.08141i
$411$		0			0
$412$	−1.91727	+	2.63890i	−0.0944573	+	0.130009i
$413$	−4.03086	−	4.03086i	−0.198346	−	0.198346i
$414$		0			0
$415$	−32.4078	+	10.5299i	−1.59084	+	0.516894i
$416$	−5.15883	+	0.817078i	−0.252932	+	0.0400606i
$417$		0			0
$418$	9.49850	+	3.08625i	0.464587	+	0.150953i
$419$		−	15.4578i		−	0.755163i	−0.925976	−	0.377581i	$-0.876756\pi$
$419$		−	15.4578i		−	0.755163i	0.925976	−	0.377581i	$-0.123244\pi$
$420$		0			0
$421$	−19.0239	+	9.69316i	−0.927168	+	0.472416i	−0.851286	−	0.524701i	$-0.824177\pi$
$421$	−19.0239	+	9.69316i	−0.927168	+	0.472416i	−0.0758813	+	0.997117i	$0.524177\pi$
$422$	8.77455	−	17.2210i	0.427139	−	0.838307i
$423$		0			0
$424$	−2.62572	+	2.62572i	−0.127516	+	0.127516i
$425$	1.87652	+	0.956133i	0.0910245	+	0.0463793i
$426$		0			0
$427$	−0.874071	−	1.71546i	−0.0422993	−	0.0830170i
$428$	0.106904	+	0.0776700i	0.00516738	+	0.00375432i
$429$		0			0
$430$	−6.71566	−	9.24332i	−0.323858	−	0.445752i
$431$	5.97602	+	8.22528i	0.287855	+	0.396198i	0.928316	−	0.371793i	$-0.121257\pi$
$431$	5.97602	+	8.22528i	0.287855	+	0.396198i	−0.640461	+	0.767991i	$0.721257\pi$
$432$		0			0
$433$	−16.6045	−	12.0639i	−0.797962	−	0.579754i	0.112353	−	0.993668i	$-0.464161\pi$
$433$	−16.6045	−	12.0639i	−0.797962	−	0.579754i	−0.910316	+	0.413915i	$0.864161\pi$
$434$	−7.36762	−	14.4598i	−0.353657	−	0.694091i
$435$		0			0
$436$	0.00943141	+	0.00480554i	0.000451683	+	0.000230144i
$437$	−5.75184	+	5.75184i	−0.275148	+	0.275148i
$438$		0			0
$439$	−1.86410	+	3.65850i	−0.0889687	+	0.174611i	−0.931203	−	0.364500i	$-0.881240\pi$
$439$	−1.86410	+	3.65850i	−0.0889687	+	0.174611i	0.842235	+	0.539111i	$0.181240\pi$
$440$	−41.7248	+	21.2599i	−1.98915	+	1.01352i
$441$		0			0
$442$			0.943390i			0.0448725i
$443$	−6.70132	−	2.17739i	−0.318389	−	0.103451i	0.145463	−	0.989364i	$-0.453533\pi$
$443$	−6.70132	−	2.17739i	−0.318389	−	0.103451i	−0.463852	+	0.885913i	$0.653533\pi$
$444$		0			0
$445$	49.8274	−	7.89189i	2.36205	−	0.374111i
$446$	3.52420	−	1.14508i	0.166875	−	0.0542211i
$447$		0			0
$448$	10.8606	+	10.8606i	0.513116	+	0.513116i
$449$	8.08754	−	11.1316i	0.381675	−	0.525330i	−0.574352	−	0.818608i	$-0.694746\pi$
$449$	8.08754	−	11.1316i	0.381675	−	0.525330i	0.956027	+	0.293278i	$0.0947461\pi$
$450$		0			0
$451$	28.5119	−	3.15078i	1.34257	−	0.148364i
$452$	1.79347			0.0843577
$453$		0			0
$454$	−14.9313	−	14.9313i	−0.700762	−	0.700762i
$455$	−4.47365	−	13.7685i	−0.209728	−	0.645477i
$456$		0			0
$457$	−1.52547	+	0.241611i	−0.0713587	+	0.0113021i	−0.192012	−	0.981393i	$-0.561501\pi$
$457$	−1.52547	+	0.241611i	−0.0713587	+	0.0113021i	0.120653	+	0.992695i	$0.461501\pi$
$458$	−15.5753	−	2.46689i	−0.727787	−	0.115270i
$459$		0			0
$460$		−	6.16689i		−	0.287533i
$461$	9.62660	−	29.6276i	0.448355	−	1.37990i	−0.430407	−	0.902635i	$-0.641630\pi$
$461$	9.62660	−	29.6276i	0.448355	−	1.37990i	0.878762	−	0.477261i	$-0.158370\pi$
$462$		0			0
$463$	−13.9772	+	27.4318i	−0.649577	+	1.27487i	0.297764	+	0.954639i	$0.403759\pi$
$463$	−13.9772	+	27.4318i	−0.649577	+	1.27487i	−0.947341	+	0.320227i	$0.896241\pi$
$464$	4.66153	+	29.4317i	0.216406	+	1.36633i
$465$		0			0
$466$	3.44962	+	1.75767i	0.159801	+	0.0814224i
$467$	0.689868	−	0.501219i	0.0319233	−	0.0231936i	−0.571709	−	0.820456i	$-0.693719\pi$
$467$	0.689868	−	0.501219i	0.0319233	−	0.0231936i	0.603632	+	0.797263i	$0.293719\pi$
$468$		0			0
$469$	−14.2667	−	10.3654i	−0.658777	−	0.478629i
$470$	4.34245	−	27.4172i	0.200302	−	1.26466i
$471$		0			0
$472$	5.87886	+	8.09156i	0.270596	+	0.372444i
$473$	−1.82749	+	11.5383i	−0.0840280	+	0.530532i
$474$		0			0
$475$	−5.49040	−	10.7755i	−0.251917	−	0.494414i
$476$	−0.164747	+	0.119696i	−0.00755117	+	0.00548624i
$477$		0			0
$478$	−12.3070	+	12.3070i	−0.562911	+	0.562911i
$479$	0.752997	+	4.75424i	0.0344053	+	0.217227i	0.998901	−	0.0468724i	$-0.0149254\pi$
$479$	0.752997	+	4.75424i	0.0344053	+	0.217227i	−0.964496	+	0.264099i	$0.914925\pi$
$480$		0			0
$481$	15.9853	−	8.14491i	0.728866	−	0.371376i
$482$	5.18426	−	15.9555i	0.236137	−	0.726754i
$483$		0			0
$484$	3.32738	+	1.08113i	0.151245	+	0.0491423i
$485$	33.6605	+	5.33131i	1.52845	+	0.242082i
$486$		0			0
$487$	−35.1859	+	11.4326i	−1.59442	+	0.518060i	−0.965720	−	0.259585i	$-0.916414\pi$
$487$	−35.1859	+	11.4326i	−1.59442	+	0.518060i	−0.628704	+	0.777645i	$0.716414\pi$
$488$	1.04386	+	3.21268i	0.0472535	+	0.145431i
$489$		0			0
$490$	10.3409	−	14.2330i	0.467154	−	0.642982i
$491$	−16.4508			−0.742413			−0.371206	−	0.928550i	$-0.621056\pi$
$491$	−16.4508			−0.742413			−0.371206	+	0.928550i	$0.621056\pi$
$492$		0			0
$493$	−2.95661			−0.133159
$494$	3.18416	−	4.38262i	0.143262	−	0.197184i
$495$		0			0
$496$	7.03618	+	21.6551i	0.315934	+	0.972344i
$497$	−0.877595	+	0.285148i	−0.0393655	+	0.0127906i
$498$		0			0
$499$	−2.45675	−	0.389111i	−0.109979	−	0.0174190i	0.101202	−	0.994866i	$-0.467731\pi$
$499$	−2.45675	−	0.389111i	−0.109979	−	0.0174190i	−0.211181	+	0.977447i	$0.567731\pi$
$500$	2.39405	+	0.777875i	0.107065	+	0.0347876i
$501$		0			0
$502$	−8.18505	+	25.1910i	−0.365317	+	1.12433i
$503$	31.9595	−	16.2842i	1.42501	−	0.726076i	0.439903	−	0.898045i	$-0.355013\pi$
$503$	31.9595	−	16.2842i	1.42501	−	0.726076i	0.985102	+	0.171969i	$0.0550129\pi$
$504$		0			0
$505$	0.937931	+	5.92187i	0.0417374	+	0.263520i
$506$	18.6582	−	18.6582i	0.829459	−	0.829459i
$507$		0			0
$508$	6.53309	−	4.74657i	0.289859	−	0.210595i
$509$	2.56872	+	5.04140i	0.113857	+	0.223456i	0.940902	−	0.338679i	$-0.109980\pi$
$509$	2.56872	+	5.04140i	0.113857	+	0.223456i	−0.827045	+	0.562135i	$0.809980\pi$
$510$		0			0
$511$	2.31423	−	14.6115i	0.102376	−	0.646374i
$512$	−14.8651	−	20.4600i	−0.656949	−	0.904213i
$513$		0			0
$514$	3.63797	−	22.9692i	0.160464	−	1.01313i
$515$	23.5913	+	17.1401i	1.03956	+	0.755283i
$516$		0			0
$517$	−22.9621	+	16.6830i	−1.00987	+	0.733715i
$518$	−14.4397	−	7.35737i	−0.634442	−	0.323264i
$519$		0			0
$520$	3.97351	+	25.0877i	0.174250	+	1.10017i
$521$	−15.5944	+	30.6057i	−0.683203	+	1.34086i	0.245268	+	0.969455i	$0.421124\pi$
$521$	−15.5944	+	30.6057i	−0.683203	+	1.34086i	−0.928471	+	0.371405i	$0.878876\pi$
$522$		0			0
$523$	1.50152	−	4.62119i	0.0656567	−	0.202070i	−0.912846	−	0.408304i	$-0.866120\pi$
$523$	1.50152	−	4.62119i	0.0656567	−	0.202070i	0.978503	+	0.206233i	$0.0661205\pi$
$524$		−	5.57027i		−	0.243338i
$525$		0			0
$526$	27.0241	+	4.28019i	1.17831	+	0.186625i
$527$	−2.23138	+	0.353416i	−0.0972004	+	0.0153950i
$528$		0			0
$529$	−0.466276	−	1.43505i	−0.0202729	−	0.0623934i
$530$	3.79540	+	3.79540i	0.164862	+	0.164862i
$531$		0			0
$532$	1.16935			0.0506978
$533$	3.15363	−	15.2364i	0.136599	−	0.659960i
$534$		0			0
$535$	0.694356	−	0.955700i	0.0300196	−	0.0413185i
$536$	21.8783	+	21.8783i	0.944999	+	0.944999i
$537$		0			0
$538$	3.56457	−	1.15820i	0.153679	−	0.0499335i
$539$	−17.7669	+	2.81399i	−0.765273	+	0.121207i
$540$		0			0
$541$	26.4078	+	8.58041i	1.13536	+	0.368901i	0.815610	−	0.578601i	$-0.196401\pi$
$541$	26.4078	+	8.58041i	1.13536	+	0.368901i	0.319749	+	0.947502i	$0.396401\pi$
$542$			14.2696i			0.612931i
$543$		0			0
$544$	0.585223	−	0.298186i	0.0250912	−	0.0127846i
$545$	0.0429608	−	0.0843152i	0.00184024	−	0.00361167i
$546$		0			0
$547$	28.2679	−	28.2679i	1.20865	−	1.20865i	0.237183	−	0.971465i	$-0.423776\pi$
$547$	28.2679	−	28.2679i	1.20865	−	1.20865i	0.971465	−	0.237183i	$-0.0762240\pi$
$548$	−0.325068	−	0.165630i	−0.0138862	−	0.00707537i
$549$		0			0
$550$	17.8101	+	34.9544i	0.759427	+	1.49046i
$551$	13.7353	+	9.97927i	0.585143	+	0.425131i
$552$		0			0
$553$	−8.75782	−	12.0541i	−0.372420	−	0.512593i
$554$	22.1295	+	30.4587i	0.940194	+	1.29407i
$555$		0			0
$556$	−2.36526	−	1.71846i	−0.100309	−	0.0728790i
$557$	−5.77051	−	11.3253i	−0.244504	−	0.479867i	0.735841	−	0.677154i	$-0.236787\pi$
$557$	−5.77051	−	11.3253i	−0.244504	−	0.479867i	−0.980346	+	0.197287i	$0.936787\pi$
$558$		0			0
$559$	5.64587	+	2.87671i	0.238795	+	0.121672i
$560$	12.9740	−	12.9740i	0.548253	−	0.548253i
$561$		0			0
$562$	1.42183	−	2.79050i	0.0599763	−	0.117710i
$563$	−7.15381	+	3.64505i	−0.301497	+	0.153621i	−0.598194	−	0.801351i	$-0.704115\pi$
$563$	−7.15381	+	3.64505i	−0.301497	+	0.153621i	0.296697	+	0.954972i	$0.404115\pi$
$564$		0			0
$565$		−	16.0333i		−	0.674526i
$566$	19.4437	+	6.31763i	0.817278	+	0.265550i
$567$		0			0
$568$	1.59908	−	0.253269i	0.0670958	−	0.0106269i
$569$	−0.559666	+	0.181847i	−0.0234624	+	0.00762341i	−0.320725	−	0.947172i	$-0.603926\pi$
$569$	−0.559666	+	0.181847i	−0.0234624	+	0.00762341i	0.297262	+	0.954796i	$0.403926\pi$
$570$		0			0
$571$	23.7361	+	23.7361i	0.993324	+	0.993324i	0.999978	−	0.00665379i	$-0.00211798\pi$
$571$	23.7361	+	23.7361i	0.993324	+	0.993324i	−0.00665379	+	0.999978i	$0.502118\pi$
$572$	2.46826	−	3.39727i	0.103203	−	0.142047i
$573$		0			0
$574$	−12.8090	+	5.78512i	−0.534639	+	0.241466i
$575$	−31.9517			−1.33248
$576$		0			0
$577$	29.1837	+	29.1837i	1.21493	+	1.21493i	0.969385	+	0.245547i	$0.0789675\pi$
$577$	29.1837	+	29.1837i	1.21493	+	1.21493i	0.245547	+	0.969385i	$0.421033\pi$
$578$	6.63781	+	20.4291i	0.276097	+	0.849738i
$579$		0			0
$580$	−12.7129	+	2.01352i	−0.527874	+	0.0836070i
$581$	−16.8608	−	2.67049i	−0.699506	−	0.110791i
$582$		0			0
$583$		−	5.48813i		−	0.227295i
$584$	−8.02082	+	24.6855i	−0.331904	+	1.02149i
$585$		0			0
$586$	15.2687	−	29.9664i	0.630742	−	1.23790i
$587$	−3.80777	−	24.0413i	−0.157164	−	0.992292i	−0.932612	−	0.360881i	$-0.882476\pi$
$587$	−3.80777	−	24.0413i	−0.157164	−	0.992292i	0.775448	−	0.631411i	$-0.217524\pi$
$588$		0			0
$589$	11.5590	+	5.88959i	0.476279	+	0.242676i
$590$	11.6961	−	8.49770i	0.481520	−	0.349845i
$591$		0			0
$592$	18.3953	+	13.3650i	0.756044	+	0.549298i
$593$	−6.57408	+	41.5071i	−0.269965	+	1.70449i	0.364220	+	0.931313i	$0.381336\pi$
$593$	−6.57408	+	41.5071i	−0.269965	+	1.70449i	−0.634185	+	0.773181i	$0.718664\pi$
$594$		0			0
$595$	1.07006	+	1.47281i	0.0438681	+	0.0603793i
$596$	0.580964	−	3.66806i	0.0237972	−	0.150250i
$597$		0			0
$598$	−6.49770	−	12.7525i	−0.265711	−	0.521487i
$599$	−13.7976	+	10.0245i	−0.563755	+	0.409592i	−0.832831	−	0.553527i	$-0.813282\pi$
$599$	−13.7976	+	10.0245i	−0.563755	+	0.409592i	0.269076	+	0.963119i	$0.413282\pi$
$600$		0			0
$601$	−17.8450	+	17.8450i	−0.727912	+	0.727912i	−0.970203	−	0.242292i	$-0.922101\pi$
$601$	−17.8450	+	17.8450i	−0.727912	+	0.727912i	0.242292	+	0.970203i	$0.422101\pi$
$602$	−0.895403	−	5.65335i	−0.0364939	−	0.230413i
$603$		0			0
$604$	−6.18671	+	3.15229i	−0.251734	+	0.128265i
$605$	9.66513	−	29.7462i	0.392944	−	1.20936i
$606$		0			0
$607$	−0.0810629	−	0.0263389i	−0.00329024	−	0.00106906i	0.307371	−	0.951590i	$-0.400551\pi$
$607$	−0.0810629	−	0.0263389i	−0.00329024	−	0.00106906i	−0.310662	+	0.950521i	$0.600551\pi$
$608$	−3.72517	−	0.590008i	−0.151075	−	0.0239280i
$609$		0			0
$610$	4.64383	−	1.50887i	0.188023	−	0.0610924i
$611$	4.75734	+	14.6416i	0.192461	+	0.592336i
$612$		0			0
$613$	−13.7750	+	18.9597i	−0.556369	+	0.765776i	−0.990859	−	0.134900i	$-0.956929\pi$
$613$	−13.7750	+	18.9597i	−0.556369	+	0.765776i	0.434490	+	0.900677i	$0.356929\pi$
$614$	−14.5838			−0.588553
$615$		0			0
$616$	−23.4601			−0.945233
$617$	24.1173	−	33.1947i	0.970927	−	1.33637i	0.0293501	−	0.999569i	$-0.490656\pi$
$617$	24.1173	−	33.1947i	0.970927	−	1.33637i	0.941577	−	0.336797i	$-0.109344\pi$
$618$		0			0
$619$	−8.20387	−	25.2489i	−0.329741	−	1.01484i	−0.969255	−	0.246059i	$-0.920864\pi$
$619$	−8.20387	−	25.2489i	−0.329741	−	1.01484i	0.639513	−	0.768780i	$-0.279136\pi$
$620$	−9.35382	+	3.03924i	−0.375658	+	0.122059i
$621$		0			0
$622$	−23.1169	−	3.66136i	−0.926904	−	0.146807i
$623$	24.0365	+	7.80992i	0.963001	+	0.312898i
$624$		0			0
$625$	−3.69513	+	11.3724i	−0.147805	+	0.454897i
$626$	16.2766	−	8.29332i	0.650542	−	0.331468i
$627$		0			0
$628$	0.670113	+	4.23092i	0.0267404	+	0.168832i
$629$	−1.59527	+	1.59527i	−0.0636075	+	0.0636075i
$630$		0			0
$631$	16.7720	−	12.1856i	0.667683	−	0.485100i	−0.201566	−	0.979475i	$-0.564603\pi$
$631$	16.7720	−	12.1856i	0.667683	−	0.485100i	0.869249	+	0.494375i	$0.164603\pi$
$632$	11.8682	+	23.2927i	0.472093	+	0.926534i
$633$		0			0
$634$	−4.76097	+	30.0596i	−0.189082	+	1.19382i
$635$	−42.4335	−	58.4047i	−1.68392	−	2.31772i
$636$		0			0
$637$	−1.52634	+	9.63693i	−0.0604758	+	0.381829i
$638$	−44.5555	−	32.3714i	−1.76397	−	1.28160i
$639$		0			0
$640$	−19.5198	+	14.1820i	−0.771588	+	0.560592i
$641$	−9.14683	−	4.66054i	−0.361278	−	0.184080i	0.263924	−	0.964544i	$-0.414983\pi$
$641$	−9.14683	−	4.66054i	−0.361278	−	0.184080i	−0.625202	+	0.780463i	$0.714983\pi$
$642$		0			0
$643$	−6.58374	−	41.5681i	−0.259637	−	1.63929i	−0.680921	−	0.732357i	$-0.738420\pi$
$643$	−6.58374	−	41.5681i	−0.259637	−	1.63929i	0.421284	−	0.906929i	$-0.361580\pi$
$644$	1.40258	−	2.75272i	0.0552695	−	0.108473i
$645$		0			0
$646$	−0.210508	+	0.647876i	−0.00828232	+	0.0254904i
$647$			15.8237i			0.622093i	0.950395	+	0.311046i	$0.100679\pi$
$647$			15.8237i			0.622093i	−0.950395	+	0.311046i	$0.899321\pi$
$648$		0			0
$649$	−14.6001	−	2.31242i	−0.573102	−	0.0907705i
$650$	21.0169	−	3.32875i	0.824350	−	0.130564i
$651$		0			0
$652$	0.236852	+	0.728955i	0.00927583	+	0.0285481i
$653$	27.7138	+	27.7138i	1.08452	+	1.08452i	0.996081	+	0.0884422i	$0.0281889\pi$
$653$	27.7138	+	27.7138i	1.08452	+	1.08452i	0.0884422	+	0.996081i	$0.471811\pi$
$654$		0			0
$655$	−49.7972			−1.94574
$656$	19.0203	−	5.20550i	0.742616	−	0.203241i
$657$		0			0
$658$	8.17404	−	11.2506i	0.318657	−	0.438594i
$659$	−25.4024	−	25.4024i	−0.989538	−	0.989538i	0.0104074	−	0.999946i	$-0.496687\pi$
$659$	−25.4024	−	25.4024i	−0.989538	−	0.989538i	−0.999946	+	0.0104074i	$0.996687\pi$
$660$		0			0
$661$	23.3250	−	7.57876i	0.907238	−	0.294779i	0.182017	−	0.983295i	$-0.441738\pi$
$661$	23.3250	−	7.57876i	0.907238	−	0.294779i	0.725221	+	0.688516i	$0.241738\pi$
$662$	1.41536	−	0.224171i	0.0550096	−	0.00871266i
$663$		0			0
$664$	28.4857	+	9.25557i	1.10546	+	0.359186i
$665$		−	10.4538i		−	0.405381i
$666$		0			0
$667$	39.9666	−	20.3640i	1.54751	−	0.788498i
$668$	0.808375	−	1.58652i	0.0312770	−	0.0613845i
$669$		0			0
$670$	31.6244	−	31.6244i	1.22176	−	1.22176i
$671$	−4.44839	−	2.26657i	−0.171728	−	0.0874998i
$672$		0			0
$673$	3.77384	+	7.40657i	0.145471	+	0.285502i	0.952232	−	0.305375i	$-0.0987818\pi$
$673$	3.77384	+	7.40657i	0.145471	+	0.285502i	−0.806762	+	0.590877i	$0.798782\pi$
$674$	−9.62341	−	6.99182i	−0.370680	−	0.269315i
$675$		0			0
$676$	1.60877	+	2.21428i	0.0618758	+	0.0851648i
$677$	−23.9553	−	32.9717i	−0.920678	−	1.26720i	−0.963386	−	0.268117i	$-0.913598\pi$
$677$	−23.9553	−	32.9717i	−0.920678	−	1.26720i	0.0427079	−	0.999088i	$-0.486402\pi$
$678$		0			0
$679$	13.8126	+	10.0354i	0.530078	+	0.385124i
$680$	−1.45010	−	2.84598i	−0.0556087	−	0.109138i
$681$		0			0
$682$	−37.4958	−	19.1051i	−1.43579	−	0.731571i
$683$	−26.6543	+	26.6543i	−1.01990	+	1.01990i	−0.0201019	+	0.999798i	$0.506399\pi$
$683$	−26.6543	+	26.6543i	−1.01990	+	1.01990i	−0.999798	+	0.0201019i	$0.993601\pi$
$684$		0			0
$685$	−1.48071	+	2.90605i	−0.0565749	+	0.111034i
$686$	21.5433	−	10.9769i	0.822527	−	0.419099i
$687$		0			0
$688$			8.03083i			0.306172i
$689$	−2.83112	−	0.919887i	−0.107857	−	0.0350449i
$690$		0			0
$691$	−46.6639	+	7.39084i	−1.77518	+	0.281161i	−0.956211	−	0.292678i	$-0.905454\pi$
$691$	−46.6639	+	7.39084i	−1.77518	+	0.281161i	−0.818968	+	0.573839i	$0.805454\pi$
$692$	1.26869	−	0.412222i	0.0482283	−	0.0156703i
$693$		0			0
$694$	6.13862	+	6.13862i	0.233019	+	0.233019i
$695$	−15.3628	+	21.1450i	−0.582743	+	0.802077i
$696$		0			0
$697$	0.214909	+	1.94475i	0.00814027	+	0.0736626i
$698$	−4.69963			−0.177884
$699$		0			0
$700$	3.24789	+	3.24789i	0.122759	+	0.122759i
$701$	7.16445	+	22.0499i	0.270597	+	0.832813i	0.990351	+	0.138583i	$0.0442549\pi$
$701$	7.16445	+	22.0499i	0.270597	+	0.832813i	−0.719753	+	0.694230i	$0.755745\pi$
$702$		0			0
$703$	12.7954	−	2.02659i	0.482588	−	0.0764344i
$704$	39.3379	+	6.23051i	1.48260	+	0.234821i
$705$		0			0
$706$			4.46935i			0.168206i
$707$	−0.928190	+	2.85667i	−0.0349082	+	0.107436i
$708$		0			0
$709$	3.28431	−	6.44583i	0.123345	−	0.242078i	−0.821074	−	0.570821i	$-0.806625\pi$
$709$	3.28431	−	6.44583i	0.123345	−	0.242078i	0.944419	+	0.328743i	$0.106625\pi$
$710$	−0.366092	−	2.31141i	−0.0137392	−	0.0867458i
$711$		0			0
$712$	−39.5100	−	20.1313i	−1.48070	−	0.754454i
$713$	27.7289	−	20.1462i	1.03846	−	0.754482i
$714$		0			0
$715$	−30.3710	−	22.0658i	−1.13581	−	0.825215i
$716$	−0.960881	+	6.06677i	−0.0359098	+	0.226726i
$717$		0			0
$718$	11.1428	+	15.3368i	0.415846	+	0.572363i
$719$	−3.36289	+	21.2325i	−0.125415	+	0.791837i	0.842156	+	0.539235i	$0.181286\pi$
$719$	−3.36289	+	21.2325i	−0.125415	+	0.791837i	−0.967570	+	0.252602i	$0.918714\pi$
$720$		0			0
$721$	6.63219	+	13.0164i	0.246996	+	0.484757i
$722$	−16.3651	+	11.8899i	−0.609046	+	0.442497i
$723$		0			0
$724$	0.663474	−	0.663474i	0.0246578	−	0.0246578i
$725$	10.4324	+	65.8676i	0.387450	+	2.44626i
$726$		0			0
$727$	33.2699	−	16.9518i	1.23391	−	0.628709i	0.289406	−	0.957206i	$-0.406542\pi$
$727$	33.2699	−	16.9518i	1.23391	−	0.628709i	0.944505	+	0.328498i	$0.106542\pi$
$728$	−3.93223	+	12.1022i	−0.145738	+	0.448536i
$729$		0			0
$730$	35.6821	+	11.5938i	1.32066	+	0.429107i
$731$	−0.787008	−	0.124650i	−0.0291085	−	0.00461034i
$732$		0			0
$733$	12.3995	−	4.02883i	0.457984	−	0.148808i	−0.0709338	−	0.997481i	$-0.522598\pi$
$733$	12.3995	−	4.02883i	0.457984	−	0.148808i	0.528918	+	0.848673i	$0.322598\pi$
$734$	−6.91954	−	21.2962i	−0.255405	−	0.786056i
$735$		0			0
$736$	−5.85708	+	8.06158i	−0.215895	+	0.297154i
$737$	−45.7287			−1.68444
$738$		0			0
$739$	−7.51921			−0.276599			−0.138299	−	0.990390i	$-0.544164\pi$
$739$	−7.51921			−0.276599			−0.138299	+	0.990390i	$0.544164\pi$
$740$	−5.77294	+	7.94577i	−0.212217	+	0.292092i
$741$		0			0
$742$	0.830942	+	2.55738i	0.0305048	+	0.0938842i
$743$	24.0292	−	7.80755i	0.881545	−	0.286431i	0.166946	−	0.985966i	$-0.446609\pi$
$743$	24.0292	−	7.80755i	0.881545	−	0.286431i	0.714599	+	0.699535i	$0.246609\pi$
$744$		0			0
$745$	−32.7919	−	5.19372i	−1.20140	−	0.190283i
$746$	−3.61784	−	1.17551i	−0.132459	−	0.0430384i
$747$		0			0
$748$	−0.163179	+	0.502213i	−0.00596641	+	0.0183627i
$749$	0.527303	−	0.268674i	0.0192672	−	0.00981715i
$750$		0			0
$751$	3.97360	+	25.0883i	0.144999	+	0.915486i	0.947713	+	0.319123i	$0.103388\pi$
$751$	3.97360	+	25.0883i	0.144999	+	0.915486i	−0.802715	+	0.596363i	$0.796612\pi$
$752$	−13.7968	+	13.7968i	−0.503117	+	0.503117i
$753$		0			0
$754$	−24.1673	+	17.5586i	−0.880122	+	0.639446i
$755$	28.1809	+	55.3082i	1.02561	+	2.01287i
$756$		0			0
$757$	2.10412	−	13.2849i	0.0764754	−	0.482847i	−0.919490	−	0.393113i	$-0.871398\pi$
$757$	2.10412	−	13.2849i	0.0764754	−	0.482847i	0.995966	−	0.0897341i	$-0.0286017\pi$
$758$	23.8562	+	32.8352i	0.866496	+	1.19263i
$759$		0			0
$760$	−2.86925	+	18.1157i	−0.104079	+	0.657127i
$761$	−6.67949	−	4.85293i	−0.242131	−	0.175919i	0.460101	−	0.887867i	$-0.347813\pi$
$761$	−6.67949	−	4.85293i	−0.242131	−	0.175919i	−0.702232	+	0.711948i	$0.747813\pi$
$762$		0			0
$763$	0.0383529	−	0.0278650i	0.00138847	−	0.00100878i
$764$	2.22739	+	1.13491i	0.0805841	+	0.0410596i
$765$		0			0
$766$	−0.499575	−	3.15419i	−0.0180504	−	0.113966i
$767$	−3.64006	+	7.14403i	−0.131435	+	0.257956i
$768$		0			0
$769$	13.5745	−	41.7779i	0.489508	−	1.50655i	−0.335837	−	0.941920i	$-0.609019\pi$
$769$	13.5745	−	41.7779i	0.489508	−	1.50655i	0.825344	−	0.564630i	$-0.190981\pi$
$770$			33.9108i			1.22206i
$771$		0			0
$772$	−0.480621	−	0.0761228i	−0.0172979	−	0.00273972i
$773$	34.7813	−	5.50882i	1.25100	−	0.198139i	0.504433	−	0.863451i	$-0.331702\pi$
$773$	34.7813	−	5.50882i	1.25100	−	0.198139i	0.746565	+	0.665312i	$0.231702\pi$
$774$		0			0
$775$	15.7468	+	48.4637i	0.565642	+	1.74087i
$776$	−21.1818	−	21.1818i	−0.760383	−	0.760383i
$777$		0			0
$778$	−44.0542			−1.57942
$779$	5.56560	−	9.75992i	0.199408	−	0.349685i
$780$		0			0
$781$	−1.40646	+	1.93583i	−0.0503272	+	0.0692694i
$782$	1.27265	+	1.27265i	0.0455097	+	0.0455097i
$783$		0			0
$784$	−11.7608	+	3.82130i	−0.420027	+	0.136475i
$785$	37.8237	−	5.99069i	1.34999	−	0.213817i
$786$		0			0
$787$	−23.1388	−	7.51826i	−0.824810	−	0.267997i	−0.133952	−	0.990988i	$-0.542767\pi$
$787$	−23.1388	−	7.51826i	−0.824810	−	0.267997i	−0.690858	+	0.722991i	$0.742767\pi$
$788$			1.30809i			0.0465988i
$789$		0			0
$790$	33.6689	−	17.1551i	1.19788	−	0.610352i
$791$	3.64658	−	7.15681i	0.129657	−	0.254467i
$792$		0			0
$793$	−1.91485	+	1.91485i	−0.0679983	+	0.0679983i
$794$	−38.9057	−	19.8234i	−1.38071	−	0.703507i
$795$		0			0
$796$	1.35659	+	2.66246i	0.0480831	+	0.0943684i
$797$	−31.9272	−	23.1965i	−1.13092	−	0.821661i	−0.145090	−	0.989418i	$-0.546347\pi$
$797$	−31.9272	−	23.1965i	−1.13092	−	0.821661i	−0.985828	+	0.167758i	$0.946347\pi$
$798$		0			0
$799$	−1.13792	−	1.56621i	−0.0402566	−	0.0554084i
$800$	−8.70795	−	11.9855i	−0.307873	−	0.423750i
$801$		0			0
$802$	−8.24809	−	5.99259i	−0.291250	−	0.211606i
$803$	−17.4158	−	34.1804i	−0.614590	−	1.20620i
$804$		0			0
$805$	−24.6089	−	12.5389i	−0.867349	−	0.441936i
$806$	−16.1404	+	16.1404i	−0.568522	+	0.568522i
$807$		0			0
$808$	2.39256	−	4.69566i	0.0841699	−	0.165193i
$809$	−5.75888	+	2.93430i	−0.202472	+	0.103164i	−0.552286	−	0.833654i	$-0.686245\pi$
$809$	−5.75888	+	2.93430i	−0.202472	+	0.103164i	0.349815	+	0.936819i	$0.386245\pi$
$810$		0			0
$811$		−	32.7119i		−	1.14867i	−0.818620	−	0.574336i	$-0.805260\pi$
$811$		−	32.7119i		−	1.14867i	0.818620	−	0.574336i	$-0.194740\pi$
$812$	−6.13262	−	1.99261i	−0.215213	−	0.0699269i
$813$		0			0
$814$	−41.5066	+	6.57400i	−1.45481	+	0.230419i
$815$	6.51673	−	2.11742i	0.228271	−	0.0741698i
$816$		0			0
$817$	3.23541	+	3.23541i	0.113193	+	0.113193i
$818$	−5.20689	+	7.16667i	−0.182055	+	0.250577i
$819$		0			0
$820$	2.24849	+	8.21569i	0.0785206	+	0.286904i
$821$	−42.4481			−1.48145			−0.740725	−	0.671808i	$-0.765518\pi$
$821$	−42.4481			−1.48145			−0.740725	+	0.671808i	$0.765518\pi$
$822$		0			0
$823$	1.50529	+	1.50529i	0.0524710	+	0.0524710i	0.732855	−	0.680384i	$-0.238187\pi$
$823$	1.50529	+	1.50529i	0.0524710	+	0.0524710i	−0.680384	+	0.732855i	$0.738187\pi$
$824$	−7.92053	−	24.3769i	−0.275925	−	0.849209i
$825$		0			0
$826$	7.15350	−	1.13300i	0.248902	−	0.0394222i
$827$	51.3821	+	8.13812i	1.78673	+	0.282990i	0.960080	−	0.279726i	$-0.0902435\pi$
$827$	51.3821	+	8.13812i	1.78673	+	0.282990i	0.826650	+	0.562716i	$0.190243\pi$
$828$		0			0
$829$		−	25.8047i		−	0.896234i	−0.893975	−	0.448117i	$-0.852095\pi$
$829$		−	25.8047i		−	0.896234i	0.893975	−	0.448117i	$-0.147905\pi$
$830$	13.3786	−	41.1752i	0.464379	−	1.42921i
$831$		0			0
$832$	9.80766	−	19.2486i	0.340020	−	0.667326i
$833$	−0.191938	−	1.21185i	−0.00665025	−	0.0419880i
$834$		0			0
$835$	−14.1833	−	7.22673i	−0.490832	−	0.250091i
$836$	2.45315	−	1.78232i	0.0848440	−	0.0616428i
$837$		0			0
$838$	15.8888	+	11.5439i	0.548869	+	0.398777i
$839$	8.15795	−	51.5073i	0.281644	−	1.77823i	−0.289299	−	0.957239i	$-0.593422\pi$
$839$	8.15795	−	51.5073i	0.281644	−	1.77823i	0.570943	−	0.820990i	$-0.306578\pi$
$840$		0			0
$841$	−37.9834	−	52.2797i	−1.30977	−	1.80275i
$842$	4.24362	−	26.7932i	0.146245	−	0.923353i
$843$		0			0
$844$	−2.66405	−	5.22850i	−0.0917005	−	0.179972i
$845$	19.7953	−	14.3821i	0.680980	−	0.494761i
$846$		0			0
$847$	11.0797	−	11.0797i	0.380701	−	0.380701i
$848$	−0.590194	−	3.72634i	−0.0202674	−	0.127963i
$849$		0			0
$850$	−2.38418	+	1.21480i	−0.0817766	+	0.0416672i
$851$	10.5768	−	32.5520i	0.362567	−	1.11587i
$852$		0			0
$853$	1.08259	+	0.351756i	0.0370673	+	0.0120439i	0.327492	−	0.944854i	$-0.393797\pi$
$853$	1.08259	+	0.351756i	0.0370673	+	0.0120439i	−0.290425	+	0.956898i	$0.593797\pi$
$854$	2.41605	+	0.382664i	0.0826755	+	0.0130945i
$855$		0			0
$856$	−0.987523	+	0.320866i	−0.0337529	+	0.0109670i
$857$	7.83870	+	24.1250i	0.267765	+	0.824095i	0.991044	+	0.133539i	$0.0426342\pi$
$857$	7.83870	+	24.1250i	0.267765	+	0.824095i	−0.723279	+	0.690556i	$0.757366\pi$
$858$		0			0
$859$	−19.3856	+	26.6820i	−0.661428	+	0.910378i	−0.999528	−	0.0307324i	$-0.990216\pi$
$859$	−19.3856	+	26.6820i	−0.661428	+	0.910378i	0.338099	+	0.941110i	$0.390216\pi$
$860$	−3.46887			−0.118288
$861$		0			0
$862$	−12.9175			−0.439972
$863$	−2.84191	+	3.91155i	−0.0967396	+	0.133151i	−0.854643	−	0.519216i	$-0.826224\pi$
$863$	−2.84191	+	3.91155i	−0.0967396	+	0.133151i	0.757903	+	0.652367i	$0.226224\pi$
$864$		0			0
$865$	−3.68520	−	11.3419i	−0.125300	−	0.385635i
$866$	24.8005	−	8.05818i	0.842756	−	0.273828i
$867$		0			0
$868$	−4.86652	−	0.770781i	−0.165180	−	0.0261620i
$869$	−36.7456	−	11.9394i	−1.24651	−	0.405015i
$870$		0			0
$871$	−7.66477	+	23.5897i	−0.259711	+	0.799307i
$872$	−0.0741111	+	0.0377615i	−0.00250972	+	0.00127877i
$873$		0			0
$874$	−1.61674	−	10.2077i	−0.0546870	−	0.345280i
$875$	7.97182	−	7.97182i	0.269497	−	0.269497i
$876$		0			0
$877$	0.997552	−	0.724764i	0.0336850	−	0.0244736i	−0.570815	−	0.821078i	$-0.693373\pi$
$877$	0.997552	−	0.724764i	0.0336850	−	0.0244736i	0.604500	+	0.796605i	$0.293373\pi$
$878$	−2.36840	−	4.64825i	−0.0799296	−	0.156871i
$879$		0			0
$880$	7.44294	−	46.9929i	0.250901	−	1.58413i
$881$	−23.2592	−	32.0135i	−0.783622	−	1.07856i	−0.994873	−	0.101131i	$-0.967754\pi$
$881$	−23.2592	−	32.0135i	−0.783622	−	1.07856i	0.211251	−	0.977432i	$-0.432246\pi$
$882$		0			0
$883$	−0.703339	+	4.44071i	−0.0236692	+	0.149442i	−0.996693	−	0.0812653i	$-0.974104\pi$
$883$	−0.703339	+	4.44071i	−0.0236692	+	0.149442i	0.973023	+	0.230707i	$0.0741039\pi$
$884$	0.231722	+	0.168356i	0.00779365	+	0.00566242i
$885$		0			0
$886$	7.24265	−	5.26209i	0.243321	−	0.176783i
$887$	26.7808	+	13.6455i	0.899212	+	0.458171i	0.841559	−	0.540165i	$-0.181638\pi$
$887$	26.7808	+	13.6455i	0.899212	+	0.458171i	0.0576530	+	0.998337i	$0.481638\pi$
$888$		0			0
$889$	−5.65768	−	35.7212i	−0.189752	−	1.19805i
$890$	−29.0992	+	57.1104i	−0.975407	+	1.91434i
$891$		0			0
$892$	0.347659	−	1.06999i	0.0116405	−	0.0358258i
$893$			11.1167i			0.372007i
$894$		0			0
$895$	54.2359	+	8.59011i	1.81290	+	0.287136i
$896$	−11.9386	+	1.89089i	−0.398841	+	0.0631702i
$897$		0			0
$898$	5.40214	+	16.6261i	0.180272	+	0.554820i
$899$	−50.5846	−	50.5846i	−1.68709	−	1.68709i
$900$		0			0
$901$	0.374336			0.0124709
$902$	−18.0541	+	31.6599i	−0.601135	+	1.05416i
$903$		0			0
$904$	−8.28360	+	11.4014i	−0.275508	+	0.379205i
$905$	−5.93134	−	5.93134i	−0.197164	−	0.197164i
$906$		0			0
$907$	44.9026	−	14.5898i	1.49097	−	0.484445i	0.553599	−	0.832783i	$-0.313254\pi$
$907$	44.9026	−	14.5898i	1.49097	−	0.484445i	0.937369	+	0.348339i	$0.113254\pi$
$908$	−6.33216	+	1.00291i	−0.210140	+	0.0332829i
$909$		0			0
$910$	17.4933	+	5.68392i	0.579897	+	0.188420i
$911$			58.9483i			1.95305i	0.215414	+	0.976523i	$0.430890\pi$
$911$			58.9483i			1.95305i	−0.215414	+	0.976523i	$0.569110\pi$
$912$		0			0
$913$	−39.4423	+	20.0968i	−1.30535	+	0.665108i
$914$	0.890876	−	1.74844i	0.0294676	−	0.0578334i
$915$		0			0
$916$	−3.38548	+	3.38548i	−0.111859	+	0.111859i
$917$	−22.2281	−	11.3258i	−0.734036	−	0.374010i
$918$		0			0
$919$	5.62090	+	11.0316i	0.185416	+	0.363900i	0.964939	−	0.262474i	$-0.0845383\pi$
$919$	5.62090	+	11.0316i	0.185416	+	0.363900i	−0.779523	+	0.626374i	$0.784538\pi$
$920$	39.2040	+	28.4834i	1.29252	+	0.939069i
$921$		0			0
$922$	23.2646	+	32.0209i	0.766177	+	1.05455i
$923$	0.762880	+	1.05001i	0.0251105	+	0.0345616i
$924$		0			0
$925$	41.1683	+	29.9106i	1.35361	+	0.983453i
$926$	−17.7585	−	34.8530i	−0.583581	−	1.14534i
$927$		0			0
$928$	18.5311	+	9.44207i	0.608313	+	0.309951i
$929$	41.7616	−	41.7616i	1.37015	−	1.37015i	0.509945	−	0.860207i	$-0.329666\pi$
$929$	41.7616	−	41.7616i	1.37015	−	1.37015i	0.860207	−	0.509945i	$-0.170334\pi$
$930$		0			0
$931$	−3.19860	+	6.27761i	−0.104830	+	0.205740i
$932$	1.04734	−	0.533648i	0.0343069	−	0.0174802i
$933$		0			0
$934$			1.08341i			0.0354504i
$935$	4.48970	+	1.45879i	0.146829	+	0.0477076i
$936$		0			0
$937$	14.8935	−	2.35889i	0.486549	−	0.0770617i	0.0916592	−	0.995790i	$-0.470783\pi$
$937$	14.8935	−	2.35889i	0.486549	−	0.0770617i	0.394889	+	0.918729i	$0.370783\pi$
$938$	21.3088	−	6.92365i	0.695757	−	0.226065i
$939$		0			0
$940$	−5.95944	−	5.95944i	−0.194376	−	0.194376i
$941$	−11.2887	+	15.5376i	−0.368002	+	0.506511i	−0.952356	−	0.304987i	$-0.901348\pi$
$941$	−11.2887	+	15.5376i	−0.368002	+	0.506511i	0.584354	+	0.811499i	$0.301348\pi$
$942$		0			0
$943$	−16.2998	−	24.8083i	−0.530793	−	0.807870i
$944$	−10.1619			−0.330740
$945$		0			0
$946$	−10.4952	−	10.4952i	−0.341230	−	0.341230i
$947$	10.9296	+	33.6378i	0.355164	+	1.09308i	0.955914	+	0.293646i	$0.0948686\pi$
$947$	10.9296	+	33.6378i	0.355164	+	1.09308i	−0.600750	+	0.799437i	$0.705131\pi$
$948$		0			0
$949$	−20.5515	+	3.25504i	−0.667131	+	0.105663i
$950$	15.1762	+	2.40367i	0.492380	+	0.0779854i
$951$		0			0
$952$		−	1.60017i		−	0.0518618i
$953$	1.20952	−	3.72252i	0.0391802	−	0.120584i	−0.929553	−	0.368688i	$-0.879807\pi$
$953$	1.20952	−	3.72252i	0.0391802	−	0.120584i	0.968734	+	0.248103i	$0.0798072\pi$
$954$		0			0
$955$	10.1459	−	19.9125i	0.328314	−	0.644352i
$956$	0.826645	+	5.21923i	0.0267356	+	0.168802i
$957$		0			0
$958$	−5.44913	−	2.77647i	−0.176053	−	0.0897037i
$959$	−1.32189	+	0.960409i	−0.0426861	+	0.0310132i
$960$		0			0
$961$	−19.1436	−	13.9086i	−0.617535	−	0.448666i
$962$	−3.56581	+	22.5136i	−0.114966	+	0.725868i
$963$		0			0
$964$	−2.99393	−	4.12079i	−0.0964279	−	0.132722i
$965$	−0.680525	+	4.29667i	−0.0219069	+	0.138315i
$966$		0			0
$967$	−15.2042	−	29.8398i	−0.488933	−	0.959584i	−0.995261	−	0.0972434i	$-0.968997\pi$
$967$	−15.2042	−	29.8398i	−0.488933	−	0.959584i	0.506328	−	0.862341i	$-0.331003\pi$
$968$	−22.2413	+	16.1593i	−0.714863	+	0.519378i
$969$		0			0
$970$	−30.6176	+	30.6176i	−0.983073	+	0.983073i
$971$	−3.19917	−	20.1988i	−0.102666	−	0.648209i	−0.984331	−	0.176332i	$-0.943577\pi$
$971$	−3.19917	−	20.1988i	−0.102666	−	0.648209i	0.881665	−	0.471877i	$-0.156423\pi$
$972$		0			0
$973$	−11.6667	+	5.94447i	−0.374017	+	0.190571i
$974$	14.5255	−	44.7048i	0.465426	−	1.43243i
$975$		0			0
$976$	−3.26412	−	1.06058i	−0.104482	−	0.0339483i
$977$	6.07624	+	0.962381i	0.194396	+	0.0307893i	0.252873	−	0.967499i	$-0.418624\pi$
$977$	6.07624	+	0.962381i	0.194396	+	0.0307893i	−0.0584771	+	0.998289i	$0.518624\pi$
$978$		0			0
$979$	62.3293	−	20.2520i	1.99205	−	0.647257i
$980$	−1.65059	−	5.08000i	−0.0527262	−	0.162275i
$981$		0			0
$982$	12.2854	−	16.9094i	0.392044	−	0.539602i
$983$	21.3411			0.680674			0.340337	−	0.940304i	$-0.389459\pi$
$983$	21.3411			0.680674			0.340337	+	0.940304i	$0.389459\pi$
$984$		0			0
$985$	11.6941			0.372605
$986$	2.20800	−	3.03905i	0.0703170	−	0.0967831i
$987$		0			0
$988$	−0.508249	−	1.56423i	−0.0161696	−	0.0497648i
$989$	11.4971	−	3.73563i	0.365586	−	0.118786i
$990$		0			0
$991$	39.8821	+	6.31670i	1.26690	+	0.200657i	0.753473	−	0.657479i	$-0.228377\pi$
$991$	39.8821	+	6.31670i	1.26690	+	0.200657i	0.513423	+	0.858136i	$0.328377\pi$
$992$	15.1142	+	4.91090i	0.479876	+	0.155921i
$993$		0			0
$994$	0.362290	−	1.11501i	0.0114911	−	0.0353661i
$995$	23.8019	−	12.1277i	0.754572	−	0.384474i
$996$		0			0
$997$	4.43858	+	28.0241i	0.140571	+	0.887531i	0.952669	+	0.304010i	$0.0983255\pi$
$997$	4.43858	+	28.0241i	0.140571	+	0.887531i	−0.812098	+	0.583521i	$0.801674\pi$
$998$	2.23466	−	2.23466i	0.0707370	−	0.0707370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.172.1		24
3.2	odd	2		41.2.g.a.8.3	✓	24
12.11	even	2		656.2.bs.d.49.3		24
41.36	even	20	inner	369.2.u.a.118.1		24
123.35	even	40		1681.2.a.m.1.5		24
123.47	even	40		1681.2.a.m.1.6		24
123.77	odd	20		41.2.g.a.36.3	yes	24
492.323	even	20		656.2.bs.d.241.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.3	✓	24	3.2	odd	2
41.2.g.a.36.3	yes	24	123.77	odd	20
369.2.u.a.118.1		24	41.36	even	20	inner
369.2.u.a.172.1		24	1.1	even	1	trivial
656.2.bs.d.49.3		24	12.11	even	2
656.2.bs.d.241.3		24	492.323	even	20
1681.2.a.m.1.5		24	123.35	even	40
1681.2.a.m.1.6		24	123.47	even	40

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.746800 + 1.02788i) q^{2} +(0.119203 + 0.366868i) q^{4} +(3.27974 - 1.06565i) q^{5} +(1.70635 + 0.270260i) q^{7} +(-2.88281 - 0.936683i) q^{8} +O(q^{10})\)	\(q+(-0.746800 + 1.02788i) q^{2} +(0.119203 + 0.366868i) q^{4} +(3.27974 - 1.06565i) q^{5} +(1.70635 + 0.270260i) q^{7} +(-2.88281 - 0.936683i) q^{8} +(-1.35394 + 4.16701i) q^{10} +(3.99164 - 2.03384i) q^{11} +(-0.380129 - 2.40004i) q^{13} +(-1.55210 + 1.55210i) q^{14} +(2.49153 - 1.81020i) q^{16} +(0.138725 + 0.272263i) q^{17} +(0.274489 - 1.73306i) q^{19} +(0.781908 + 1.07620i) q^{20} +(-0.890407 + 5.62181i) q^{22} +(-3.75048 - 2.72488i) q^{23} +(5.57599 - 4.05119i) q^{25} +(2.75084 + 1.40162i) q^{26} +(0.104252 + 0.658222i) q^{28} +(-4.39273 + 8.62121i) q^{29} +(-2.28469 + 7.03157i) q^{31} -2.14948i q^{32} +(-0.383454 - 0.0607331i) q^{34} +(5.88439 - 0.931996i) q^{35} +(2.28152 + 7.02179i) q^{37} +(1.57639 + 1.57639i) q^{38} -10.4531 q^{40} +(5.99000 + 2.26271i) q^{41} +(-1.53275 + 2.10964i) q^{43} +(1.22197 + 1.22197i) q^{44} +(5.60172 - 1.82011i) q^{46} +(-6.25754 + 0.991097i) q^{47} +(-3.81880 - 1.24080i) q^{49} +8.75689i q^{50} +(0.835185 - 0.425548i) q^{52} +(0.556161 - 1.09153i) q^{53} +(10.9242 - 10.9242i) q^{55} +(-4.66595 - 2.37742i) q^{56} +(-5.58110 - 10.9535i) q^{58} +(-2.66945 - 1.93947i) q^{59} +(-0.655043 - 0.901590i) q^{61} +(-5.52141 - 7.59957i) q^{62} +(7.19247 + 5.22564i) q^{64} +(-3.80433 - 7.46641i) q^{65} +(-9.09493 - 4.63410i) q^{67} +(-0.0833482 + 0.0833482i) q^{68} +(-3.43648 + 6.74448i) q^{70} +(-0.475905 + 0.242486i) q^{71} -8.56300i q^{73} +(-8.92141 - 2.89874i) q^{74} +(0.668523 - 0.105884i) q^{76} +(7.36081 - 2.39167i) q^{77} +(-6.09837 - 6.09837i) q^{79} +(6.24253 - 8.59210i) q^{80} +(-6.79914 + 4.46722i) q^{82} -9.88122 q^{83} +(0.745119 + 0.745119i) q^{85} +(-1.02381 - 3.15096i) q^{86} +(-13.4122 + 2.12429i) q^{88} +(14.4489 + 2.28848i) q^{89} -4.19804i q^{91} +(0.552606 - 1.70075i) q^{92} +(3.65440 - 7.17217i) q^{94} +(-0.946582 - 5.97648i) q^{95} +(8.80540 + 4.48657i) q^{97} +(4.12728 - 2.99864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Introduction

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